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Warm-Up

Warm-Up. 1.) Ramon has a 3 in. by 5 in. photo. He wants to enlarge both dimensions by the same amount. If x represents the amount of increase, the new dimensions can be written as (3 + x) in. and (5 + x) in. Which expression represents the perimeter of the enlarged photo: (3+x) + (5+x)

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Warm-Up

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  1. Warm-Up • 1.) Ramon has a 3 in. by 5 in. photo. He wants to enlarge both dimensions by the same amount. If x represents the amount of increase, the new dimensions can be written as (3 + x) in. and (5 + x) in. Which expression represents the perimeter of the enlarged photo: • (3+x) + (5+x) • (3+x)(5+x) • (3+x) + (3+x) + (5+x) + (5+x) • 2(3+x)(5+x) • 2. Explain how to simplify the expression you chose then simplify.

  2. “If there is no struggle, then there is no progress” Foundations:integer operations, variables Essential Question: How can we simplify a variable expression? Homework:pg. 61 #1-14 all and QUIZ NEXT CLASS!!

  3. Polynomials a number or variable or a combination of both • MONOMIALS: • A. A monomial is _______________ • B. Some examples of monomials are:

  4. POLYNOMIALS: • A. A polynomial is the ________ or ___________ of monomials. SUM Difference B. An example of a polynomial in one variable, x, would be C. How many MONOMIALS are there in the above polynomial? 4

  5. highest • The _________exponent in the polynomial determines the DEGREEE OF A POLYNOMIAL in one variable. A. Example: The degree of –7x + 9 – 4x2 is ____ because ___ is the largest exponent in the polynomial. 2 2 B. Example: Find the degree of the following polynomial: x4 + 6x3 + 7x5 + 12x Not 125

  6. IV. STANDARD FORM A. The terms of a polynomial are in STANDARD FORM if they are ordered from left to right in ______________ order; which means from the ____________ exponent to the least. Descending greatest B. To write a polynomial in Standard Form, ______________ the terms of the polynomial in ______________ order according to the ________________ of the variables. arrange Descending exponents

  7. IV. STANDARD FORM C. Example: Write 9 + x – 4x3 in standard form. D. Example: Write 3x2 – 2 + 4x – 5x3 in standard form.

  8. V. Some polynomials have SPECIAL NAMES that are determined by the following: A. Their _________ or B. Their _________ of terms exponent Total #

  9. Like Terms • Termsare the parts of an expression that are being added or subtracted. • A term includes the preceding sign (+ or -), the coefficient, and any variables (including exponents). • Like terms have all variables and exponents in common. Example: 2x2 + 3x

  10. Checkpoint • Identify the like terms in the expression. • -5x2 – x + 8 + 6x – 10 • -3x2 + 2x + x2 – 4 + 7x

  11. Combining Like Terms • In order for an expression to simplified, all like terms must be combined. • Combine like terms by adding the coefficients of any like terms. • (Be careful with the signs!)

  12. Checkpoint • Combine the like terms in the expression. • -5x2 – x + 8 + 6x – 10 • -3x2 + 2x + x2 – 4 + 7x -5x2 –x + 6x + 8 - 10 -5x2 + 5x – 2

  13. Checkpoint • Answers: • 3x • 4m + 5 • 5x • 5x – 2x • 8m – m – 3m + 5 • -x2 + 5x + x2

  14. 0 Constant 1 Linear 2 Quadratic 3 Cubic 4 Quartic 1 Monomial 2 Binomial Trinomial 3 4 Polynomial

  15. Adding Polynomials Underline, circle, double underline… LIKE terms.

  16. Subtracting Polynomials We need to distribute the negative 1st. Then rewrite using vertical method.

  17. YOU TRY! To add or subtract polynomials you just combine like terms!!! 1) 2) Attention: When subtracting, don’t forget to distribute the negative!!!!

  18. Worksheet • Make sure you put your name on your paper. • Work quietly by yourself or with your partner. • Hang on to it if you finish before class is over

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